Points: 0.5 of 1
Use long division to find the quotient $Q(x)$ and the remainder $R(x)$ when $P(x)$ is divided by $d(x)$ and express $P(x)$ in the form $d(x) \cdot Q(x)+R(x)$.
\[
\begin{array}{l}
P(x)=x^{3}+2 x^{2}-9 x+183 \\
d(x)=x+7
\end{array}
\]
\[
P(x)=(x+7)
\]
Answer
\(\boxed{Q(x) = x^{2} - 5x + 36, R(x) = -69}\)
Step 1 ：We are given a polynomial \(P(x) = x^{3} + 2x^{2} - 9x + 183\) and a divisor \(d(x) = x + 7\). We are asked to perform polynomial long division to find the quotient \(Q(x)\) and the remainder \(R(x)\) such that \(P(x) = d(x) \cdot Q(x) + R(x)\).
Step 2 ：Performing the polynomial long division, we find that the quotient is \(Q(x) = x^{2} - 5x + 36\) and the remainder is \(R(x) = -69\).
Step 3 ：Therefore, the polynomial \(P(x)\) can be expressed as \(P(x) = d(x) \cdot Q(x) + R(x)\), where \(Q(x) = x^{2} - 5x + 36\) and \(R(x) = -69\).
Step 4 ：\(\boxed{Q(x) = x^{2} - 5x + 36, R(x) = -69}\)
